A boundary element solution is given for a magnetohydrodynamic (MHD) flow problem in a rectangular duct having insulating walls, in terms of velocity and induced magnetic field. The coupled velocity and magnetic field equations are first transformed into decoupled nonhomogeneous convection-diffusion type equations and then finding particular solutions, the homogeneous equations are solved using the boundary element method (BEM). The fundamental solutions of the decoupled homogeneous equations themselves are used which contain the Hartmann number through exponential and modified Bessel functions. Thus, it is possible to increase the Hartmann number to moderate values in the calculations especially when the singularities in the integrals are taken care of with the asymptotic expansions of modified Bessel functions. The computations are carried out for the Hartmann number M <= 50 using constant boundary elements. It is found that as the number of boundary elements increases it is possible to increase the Hartmann number although it is time consuming. This is not the case in the dual reciprocity boundary element solution of MHD problems since the fundamental solution of the Laplace equation is used, Tezer-Sezgin and Aydin . The velocity and induced magnetic field contours are illustrated in terms of graphics. It is observed that as the Hartmann number increases boundary layers are formed near the boundaries which is a well known behaviour of MHD flow.